Simulate a 2-input linear system with with ode45

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Tianyi Zhu
Tianyi Zhu 2020-10-16
评论： Tianyi Zhu 2020-10-17
Hello everyone,
I am new to ode45, I know how I should use ode45 to simulate a SISO system, but now I am trying to use it on a 2-input 2-output system.
The state space equations are as followed:
And here is my code trying to define the odefunction, the plot is not matching the result using lsim(), so it should not be correct.
t = [0 50]
x0 = [0 0 0 0 0];
[t,y] = ode45(@odefun,t,x0);
plot (t,y,'green');
grid on;
function dxdt = odefun(t,x)
x1 = x(1);
x2 = x(2);
x3 = x(3);
%input u
u1 =10;
u2 =10;
dxdt = zeros(5,1);
dxdt(1) = -1/6*x1-1/3*x3+1/6*u1+1/3*u2;
dxdt(2) = x3;
dxdt(3) = 0.5*x1-0.5*x2-0.5*x3;
dxdt(4) = x1-x2-x3;
dxdt(5) = 0.5*u1 -0.5*x1;
end

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采纳的回答

Alan Stevens
Alan Stevens 2020-10-17
More like this:
tspan = [0 50];
x0 = [0; 0; 0];
u = [10; 10];
[t,x] = ode45(@(t,x) odefun(t,x,u),tspan,x0);
x = x';
My = [1 -1 -1; -1/2 0 0];
Ky = [0 0; 1/2 0];
y = My*x + Ky*u;
plot (t,y,'green');
grid on;
function dxdt = odefun(~,x,u)
M = [-1/6 0 -1/3; 0 0 1; 1/2 -1/2 -1/2];
K = [1/6 1/3; 0 0; 0 0];
dxdt = M*x + K*u;
end

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